Dipole factorization for DIS at NLO: Loop correction to theγT,L*→qq¯light-front wave functions

Abstract

The one-loop QCD corrections to the light-front wave-function for the quark-antiquark Fock state inside a transverse or longitudinal off-shell photon are explicitly calculated, both in full momentum space and in mixed space (a.k.a. dipole space). These results provide one of the main contributions to virtual NLO corrections to many DIS observables (inclusive or not) in the dipole factorization formalism at low Bjorken x.In a follow-up article, these one-loop corrections are combined with earlier results on the wavefunction for the quark-antiquark-gluon Fock state, in order to get the full set of NLO corrections to the DIS structure functions F2 and FL in the dipole factorization formalism, valid at low Bjorken x.At low Bjorken x (x Bj ), various deep inelastic scattering (DIS) observables can be studied using the dipole factorization formalism, in particular inclusive DIS structure functions [1,2] and diffractive DIS structure functions [3] as well as exclusive vector meson vector meson production [4] and deeply virtual Compton scattering. This formalism is motivated by light-front perturbation theory [1,5], which provides the light-front wave-functions (LFWF) for the fluctuation of the exchanged photon into a quark-antiquark dipole, and relies on the eikonal approximation, which allows to describe the interaction of the quark-antiquark dipole on the target, in the high-energy limit relevant for DIS at low x Bj . The dipole factorization has a remarkable versatility. Not only does it allow one to study in a unified way inclusive, diffractive and exclusive observables, but it allows one to include and study various dynamical effects from QCD. For that reason, a large part of the theoretical and phenomenological work in the literature related to the results (at low x Bj ) from the HERA collider are based on the dipole factorization.Pushing further the dipole picture, it has been possible to rederive in a more intuitive way [6-8] the BFKL equation [9][10][11], which allows one to resum large logarithms arising in perturbation theory for high-energy (or equivalently low x Bj ) semi-hard scattering processes between two dilute objects in QCD, within the leading logarithmic approximation (LL). Moreover, thanks to the use of the eikonal approximation, it is trivial to include coherent multiple scattering effects within the dipole factorization, via Wilson lines, in the case of a dense target. When such effects are relevant, one enters into the gluon saturation regime of QCD [12][13][14][15][16], also called Color Glass Condensate (CGC). In the presence of gluon saturation effects, the BFKL equation has to be replaced by a nonlinear evolution in order to perform the high-energy LL resummation, which is the B-JIMWLK evolution [17][18][19][20][21][22][23][24][25], or in a mean-field approximation the Balitsky-Kovchegov (BK) equation [17,26,27]. Using the dipole factorization in conjunction with the BK equation (modified to include running QCD coupling effects [28,29]), it has been possible to obtain successful fits [30][31...

HERA data and collinearly-improved BK dynamics

“…Derived via systematic approximations within perturbative QCD, the Colour Glass Condensate (CGC) effective theory [1][2][3][4][5] is a powerful framework for computing high-energy processes in the presence of nonlinear effects associated with high parton densities. There are intense ongoing efforts towards extending this effective theory to next-to-leading order (NLO) accuracy, as required by realistic applications to phenomenology [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. These efforts refer both to the Balitsky-JIMWLK equations [20][21][22][23][24][25][26], which govern the high-energy evolution of the scattering amplitudes, and to the impact factors, which represent cross-sections at relatively low energy.…”

Use of a running coupling in the NLO calculation of forward hadron production

“…That calculation too was based on a factorization scheme nonlocal in rapidity (similar to the one that we employed in this paper) together with the NLO impact factor for the virtual photon from Refs. [32,33].…”

“…[31], a similar problem appears in the context of deep inelastic scattering (DIS), when using the "dipole factorization" (a version of k T factorization appropriate for DIS at high energy) together with the NLO impact factor from Refs. [32,33].…”

Extracting many-body correlators of saturated gluons with precision from inclusive photon+dijet final states in deeply inelastic scattering

“…The numerical computation of the finite pieces con-stitutingX NLO;jet µν;finite , along with NLO BK/JIMWLK evolution, provide the necessary ingredients to compute photon+dijet production (and associated measurement channels) in e+A DIS to O(α 3 S ln(1/x)) accuracy. Prior NLO studies on DIS at small x focused on the crosssection for fully inclusive DIS [51][52][53][54][55][56][57][58][59], a noteworthy exception being the NLO studies of diffractive dijet and exclusive vector meson production by Boussarie et al [60][61][62]. In this regard, our work goes a step beyond by considering more differential final states.…”